Taken directly from the name of the main character of Diagnosis Murder, the act of doing a 'Doctor Sloan' involves solving, or helping to solve, a problem using information that by all accounts SHOULDN'T be useful at that point. Could also be described as a fluke of genius in unlikely circumstances.

Person A: "Fat Fuck Freddy has gone to the chinese takeaway without me and left 10 minutes ago. We'll never catch him now."